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It was shown in  that there exists an explicit bound for the number of Pachner moves needed to connect any two triangulation of any Haken 3-manifold which contains no fibred sub-manifolds as strongly simple pieces of its JSJ-decomposition. In this paper we prove a generalisation of that result to all knot complements. The explicit formula for the bound is in terms of the numbers of tetrahedra in the two triangulations. This gives a conceptually trivial algorithm for recognising any knotdoi:10.4310/mrl.2005.v12.n6.a6 fatcat:5fhpqoklgzfk5coldk5b6havue